Fault Detection Algorithm for Gaussian Mixture Noises: An Application in Lidar/IMU Integrated Localization Systems

Fault detection is crucial to ensure the reliability of localization systems. However, conventional fault detection methods usually assume that noises in the system have a Gaussian distribution, limiting their effectiveness in real-world applications. This study proposes a fault detection algorithm for an extended Kalman filter (EKF)-based localization system by modeling non-Gaussian noises as a Gaussian mixture model (GMM). The relationship between GMM-distributed noises and the measurement residual is rigorously established through error propagation, which is utilized to construct the test statistic for a chi-squared test. The proposed method is applied to an EKF-based two-dimensional light detection and ranging/inertial measurement unit integrated localization system. Experimental results in a simulated urban environment show that the proposed method exhibits a 30% improvement in the detection rate and a 17%–23% reduction in the detection delay, compared with the conventional method with Gaussian noise modeling.